Cubatures of precision $2k$ and $2k+1$ for hyperrectangles
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- by Dalton R. Hunkins PDF
- Math. Comp. 29 (1975), 1098-1104 Request permission
Abstract:
It is well known that integration formulas of precision $2k\;(2k + 1)$ for a region in n-space which is a Cartesian product of intervals can be obtained from one-dimensional Radau (Gauss) rules. The number of function evaluations in these product cubatures is ${(k + 1)^n}$. In this paper, an algorithm is given for obtaining cubatures for hyperrectangles in n-space of precision 2k, in many instances $2k + 1$, which uses $(k + 1){(k)^{n - 1}}$ nodes. The weights and nodes of these new formulas are derived from one-dimensional generalized Radau rules.References
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- Richard Franke, Minimal point cubatures of precision seven for symmetric planar regions, SIAM J. Numer. Anal. 10 (1973), 849–862. MR 343544, DOI 10.1137/0710070
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 1098-1104
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1975-0388738-X
- MathSciNet review: 0388738